27 research outputs found
Cardinality versus q-Norm Constraints for Index Tracking
Index tracking aims at replicating a given benchmark with a smaller number
of its constituents. Different quantitative models can be set up to determine the
optimal index replicating portfolio. In this paper, we propose an alternative
based on imposing a constraint on the q-norm, 0 < q < 1, of the replicating
portfolios’ asset weights: the q-norm constraint regularises the problem and
identifies a sparse model. Both approaches are challenging from an optimisation viewpoint due to either the presence of the cardinality constraint or a
non-convex constraint on the q-norm. The problem can become even more
complex when non-convex distance measures or other real-world constraints are
considered. We employ a hybrid heuristic as a flexible tool to tackle both optimisation problems. The empirical analysis on real-world financial data allows
to compare the two index tracking approaches. Moreover, we propose a strategy
to determine the optimal number of constituents and the corresponding optimal
portfolio asset weights
Cardinality versus q-Norm Constraints for Index Tracking,
Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating port- folio. In this paper, we propose an alternative based on imposing a constraint on the q-norm (0 < q < 1) of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimisation viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance mea- sures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimisation problems. The empirical analysis on real-world financial data allows to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights
Constructing Optimal Sparse Portfolios Using Regularization Methods
The ideas of Markowitz indisputably constitute a milestone in portfolio theory, even though the resulting mean-variance portfolios typically exhibit an unsatisfying out-of-sample performance, especially when the number of securities is large and that of observations is not. The bad performance is caused by estimation errors in the covariance matrix and in the expected return vector that can deposit unhindered in the portfolio weights. Recent studies show that imposing a penalty in form of a l1-norm of the asset weights regularizes the problem, thereby improving the out-of-sample performance of the optimized portfolios. Simultaneously, l1-regularization selects a subset of assets to invest in from a pool of candidates that is often very large. However, l1-regularization might lead to the construction of biased solutions. We propose to tackle this issue by considering several alternative penalties proposed in non-financial contexts. Moreover we propose a simple new type of penalty that explicitly considers funancial information. We show empirically that these alternative penalties can lead to the construction of portfolios with superior out-of-sample performance in comparison to the state-of-the art l1-regularized portfolios and several standard benchmarks, especially in high dimensional problems. The empirical analysis is conducted with various U.S.-stock market datasets